Iodine Clusters in the Atmosphere I: Computational Benchmark and Dimer Formation of Oxyacids and Oxides

The contribution of iodine-containing compounds to atmospheric new particle formation is still not fully understood, but iodic acid and iodous acid are thought to be significant contributors. While several quantum chemical studies have been carried out on clusters containing iodine, there is no comprehensive benchmark study quantifying the accuracy of the applied methods. Here, we present the first study in a series that investigate the role of iodine species in atmospheric cluster formation. In this work, we have studied the iodic acid, iodous acid, iodine tetroxide, and iodine pentoxide monomers and their dimers formed with common atmospheric precursors. We have tested the accuracy of commonly applied methods for calculating the geometry of the monomers, thermal corrections of monomers and dimers, the contribution of spin–orbit coupling to monomers and dimers, and finally, the accuracy of the electronic energy correction calculated at different levels of theory. We find that optimizing the structures either at the ωB97X-D3BJ/aug-cc-pVTZ-PP or the M06-2X/aug-cc-pVTZ-PP level achieves the best thermal contribution to the binding free energy. The electronic energy correction can then be calculated at the ZORA-DLPNO–CCSD(T0) level with the SARC-ZORA-TZVPP basis for iodine and ma-ZORA-def2-TZVPP for non-iodine atoms. We applied this methodology to calculate the binding free energies of iodine-containing dimer clusters, where we confirm the qualitative trends observed in previous studies. However, we identify that previous studies overestimate the stability of the clusters by several kcal/mol due to the neglect of relativistic effects. This means that their contributions to the currently studied nucleation pathways of new particle formation are likely overestimated.


Monomer Geometry Benchmark
The iodine oxides used a different reference than the oxy-acids due to computational limitations.For these structures we used the ωB97X-D3BJ/aug-cc-pVTZ-PP structures as their reference.This is done because higher-level methods are not practically possible for these, therefore it can not be fully evaluated.The results of this can be seen in Figure S2 The same unambigous conclusion can not be made for for I 2 O 4 and I 2 O 5 where large RMSD values can be observed for the PP based DFT methods, especially when only a double ζ basis set is used, e.g.ωB97X-D3BJ/aug-cc-pVDZ-PP has an RMSD value larger than 0.7 Å for I 2 O 4 , this difference amounts to a roughly 90 degree rotation of one of the bonds.Increasing the basis set to triple ζ generally lessens the geometry differences except for M06-2X/augcc-pVTZ-PP where the RMSD value increases from less than 0.1 Å to 0.5 Å for I 2 O 5 .
However, the majority of the pseudo-potential DFT methods still agree on the structures of the iodine oxides.
B 3 L Y P / a u g -c c -p V D Z -P P B 3 L Y P / a u g -c c -p V T Z -P P M 0 6 -2 X / a u g -c c -p V D Z -P P M 0 6 -2 X / a u g -c c -p V T Z -P P P W 9 1 / a u g -c c -p V D Z -P P P W 9 1 / a u g -c c -p V T Z -P P B 9 7 X -D 3 B J / a u g -c c -p V D Z -P P HIO 2 HIO 3 Figure S3: Root mean square deviations (RMSD) for the lowest energy structure of each monomer for a given method compared to a reference structure.For IsA and IA this was chosen to be DKH-CCSD(T)/TZVPP.RMSD was calculated using ArbAlign.The blue dashed line at 0.38 Å is added because this value has been used in our previous studies to evaluate uniqueness of cluster structures.In Figure S5, the SOC stabilization energy of iodous acid, calculated at the DKH-ωB97X-D3BJ/aug-cc-pVQZ-DK level, can be seen for structures optimized at different levels of theory.It can be observed that SOC is not very sensitive to the small geometry changes due to different levels of theory for the optimization, with stabilization energies ranging from We tested the sensitivity of the SOC stabilization for both HOIO and HOIO 2 with regards to the basis set used for the TD-DFT calculation.In Figure S6a it can be seen that the final result using 10 roots for HOIO varies between approx.−1.4 and −1.6 kcal/mol depending on the basis set used.A similar trend can be observed for all methods, where increasing the basis set size from triple ζ to quadruple ζ results in a slight decrease in the predicted SOC stabilization energy.The same can be observed for HOIO 2 in Figure S6b.To further evaluate the final methodology: ZORA-DLPNO-CCSD(T 0 )//ωB97X-D3BJ/augcc-pVTZ-PP, we compare it to results derived by using 4-component relativistic DFT: ZORA-PBE0/QZ4P which can be seen in Table S3.For the relativistic DFT we only have one structure of the IsA-SA cluster, which we compare with the structures for the subset of 5

S2.2 Monomer Spin-orbit Coupling
IsA-SA clusters calculated in the benchmark.
We observe excellent agreement in the binding free energy between the two methods.To our knowledge, no benchmarks have been made for thermal contributions of ZORA-PBE0/QZ4P.
However, a study has been conducted benchmarking the bond-lengths against experimental data for [Pt(CN) 4 ] 2 -, 1 where it, and other functional and basis set combinations, were shown to describe the bond-lengths within 1 pm.
Table S3: Binding free energies of selected IsA-SA dimers calculated using relativistic DFT, G binding Relativistic, DFT : Single-point and frequencies were calculated for an optimized structure at the PBE0/QZ4P level with SO-ZORA formalism and gaussian nuclear model in the Amsterdam Modelling Suite.For 5 optimized structures, optimized at the ωB97X-D3BJ/aug-cc-pVTZ-PP level, ZORA-DLPNO-CCSD(T 0 )/TZVPP//ωB97X-D3BJ/aug-cc-pVTZ-PP was calculated: G binding Relativistic, scalar .

S3.4 Dimer Energies
Here we present the binding energies and thermochemistry of the identified lowest free energy clusters at the ωB97X-D3BJ/aug-cc-pVTZ-PP, and ZORA-DLPNO-CCSD(T 0 )//ωB97X-D3BJ/aug-cc-pVTZ-PP level of theory.Finally we present D 0 values, which are the electronic energy with the addition of the vibrational zero-point energy.

Figure S2 :
FigureS2: Root mean square deviations (RMSD) for the lowest energy structure of each monomer for a given method compared to a reference structure.For I 2 O 4 and I 2 O 5 it chosen to be ωB97X-D3BJ/aug-cc-pVTZ-PP. RMSD was calculated using ArbAlign.The blue dashed line at 0.38 Å is added because this value has been used in our previous studies to evaluate uniqueness of cluster structures.

Figure S4 :
Figure S4: Spin-orbit coupling (SOC) stabilization of HI TD-DFT was calculated at the DKH-ωB97X-D3BJ/aug-cc-pVQZ-DK level of theory on the structure optimized at the DKH2-CCSD(T)/def2-TZVPP level.The number of roots refers to the number of states included in the calculation.The results obtained by Khanniche et al. have been marked with red dashed lines.

Figure S8 :Figure S10 :
FigureS8: ZORA-DLPNO-CCSD(T 0 )/TZVPP//ωB97X-D3BJ/aug-cc-pVTZ-PP binding free energies for the generated structures.The full distribution of binding free energies is plotted together with the combined distributions of dimers containing the acids: SA, MSA, NA, FA, the bases: AM, MA, DMA, TMA, EDA and iodine oxy-acids and lastly the distribution of dimers containing the iodine oxides.

Table S1 :
Median and standard deviations of the distributions of thermal energy contributions at different levels of theory.

Table S2 :
Median and standard deviations of the distributions of relative thermal energy contributions for each structure at different levels of theory relative to ωB97X-D3BJ/augcc-pVTZ.These are relative for each structure where the ωB97X-D3BJ/aug-cc-pVTZ was re-optimized with each level of theory.

Table S5 :
Binding energies and thermochemistry of dimer clusters at the ωB97X-D3BJ/augcc-pVTZ-PP level of theory at 298.15 K.

Table S9 :
Lowest binding free energy of iodine containing dimers, given in kcal/mol, calculated at the ZORA-DLPNO-CCSD(T 0 )/TZVPP//ωB97X-D3BJ/aug-cc-pVTZ-PP level of theory at 283.15 K and 1 atm.Rows denote the first component, and column denote second component.